Number Question
Consider a real number x such that x = ab.cd, where a, b, c and d are the digits of the number . Also, a and d is not equal to 0.
[x] = The greatest integer less than or equal to x and {x} = x – [x]
Solution
Consider a real number x such that x = ab.cd, where a, b, c and d are the digits of the number . Also, a and d is not equal to 0.
[x] = The greatest integer less than or equal to x and {x} = x – [x]
if [10{p}] = 8 and {10{p}}=9
Also, [p] is 5 less than the sum of the digits of the quantity 100{p}. Find p
a. 21.89
b. 89.12
c. 12.89
d. None of the above
We can always work with options.
Suppose option (a) is the correct answer.
x = 21.89
[x] = [21.89] = 21
{x} = x - [x] = 21.89 - 21 = 0.89
Now, note that:
[10{p}] = [10(0.89)] = [8.9] = 8
{10{p}} = {10(0.89)} = {8.9} = 8.9 - [8.9] = 8.9 - 8 = 0.9
which does not satisfy the given condition of the problem.
Hence option (a) is not the correct answer.
Next suppose option (b) is the correct answer.
x = 89.12
[x] = [89.12] = 89
{x} = x - [x] = 89.12 - 89 = 0.12
Now, note that:
[10{p}] = [10(0.12)] = [1.2] = 1
which does not satisfy the given condition of the problem.
Hence option (b) is not the correct answer.
Now suppose option (a) is the correct answer.
x = 12.89
[x] = [12.89] = 12
{x} = x - [x] = 12.89 - 12 = 0.89
Now, note that:
[10{p}] = [10(0.89)] = [8.9] = 8
{10{p}} = {10(0.89)} = {8.9} = 8.9 - [8.9] = 8.9 - 8 = 0.9
which does not satisfy the given condition of the problem.
Hence option (c) is also not the correct answer.
Therefore, option (d) is correct.
Ravi Raja